Dear Jan, Jan Bos wrote:
Is there a reason for GiNaC (or ginsh) to evaluate atan2(0,-4) as -Pi instead of +Pi the definition used by for instance C/C++? Looking at the code, inifcns_trans.cpp last shown case below, explicitly states it should. Or can I expect it to be changed in the future?
static ex atan2_eval(const ex & y, const ex & x) { if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
if (y.is_zero()) {
// atan(0, 0) -> 0 if (x.is_zero()) return _ex0;
// atan(0, x), x real and positive -> 0 if (x.info(info_flags::positive)) return _ex0;
// atan(0, x), x real and negative -> -Pi if (x.info(info_flags::negative)) return _ex_1*Pi; }
I don't suppose anybody lightly intends to change such definitions. :) Well, I looked in my notes and didn't find anything motivating that choice for atan2. I recall that back when I wrote this, CLTL 2nd edition provided guidance when choosing branch cuts of single-argument functions in the complex domain. And later at some point I realized that the C99 standard agrees with CLTL for all single-argument functions. (That appeared to be too good to be true, but it is true.) Nobody was aware of LIA-3 at that time but I'm quite sure that all of GiNaC's single-argument functions agree with LIA-3, simply because they agree with C99. Our two-argument function atan2, however, may never have been checked against any standard. I just did that with C99 and CLTL, and they both specify atan2(0,-4) to be +Pi, indeed. Maybe, we ought to change this? Before we do so: What does LIA-3 say? Our choice may be bad but I frankly admit that I don't know why +Pi is any better than -Pi, or a more symmetric choice a la Mathematica like atan2(0,x>0)=Pi/2, atan2(0,x<0)=-Pi/2, or 0 for all x. Can you explain that choice? Cheers -richy. PS: In any case, this is a good lesson how not to write comments, sigh. -- Richard B. Kreckel <http://www.ginac.de/~kreckel/>